The induced path function, monotonicity and betweenness

Manoj Changat, Joseph Mathew and Martyn Mulder

No EI 2006-23, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: The induced path function $J(u, v)$ of a graph consists of the set of all vertices lying on the induced paths between vertices $u$ and $v$. This function is a special instance of a transit function. The function $J$ satisfies betweenness if $w \\in J(u, v)$ implies $u \\notin J(w, v)$ and $x \\in J(u, v)$ implies $J(u, x \\subseteq J(u, v)$, and it is monotone if $x, y \\in J(u, v)$ implies $J(x, y) \\subseteq J(u, v)$. The induced path function of a connected graph satisfying the betweenness and monotone axioms are characterized by transit axioms.

Keywords: betweenness; house domino; induced path; long cycle; monotone; p-graph; transit function (search for similar items in EconPapers)
Date: 2006-06-28
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Citations: View citations in EconPapers (1)

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